Vertical Line Test: Determining if a Linear Graph Represents a Function

Q: What exactly is the vertical line test?

The vertical line test helps determine if a graph represents a function. Draw imaginary vertical lines anywhere on the graph - if any vertical line crosses the graph more than once, it's not a function!

Q: Why does this linear graph pass the vertical line test?

Linear graphs like this one are always functions unless they're vertical lines! Since this line has a slope (goes up from left to right), no vertical line can intersect it twice.

Q: What would make a graph NOT a function?

Common examples include:Circles - vertical lines through the middle cross twiceParabolas opening sideways - most vertical lines cross twiceVertical lines themselves - infinite intersections with one vertical line

Q: Can I tell if it's a function without drawing vertical lines?

Yes! For linear equations, if you can solve for $ y $ and get $ y = mx + b $ form, it's automatically a function. Only vertical lines (like $ x = 3 $) are not functions.

Q: Does the slope of the line matter for the vertical line test?

No! Whether the line goes up, down, or is horizontal doesn't matter. As long as it's not a vertical line, it will always pass the vertical line test and be a function.

Function Identification with Linear Graphs

Does the graph below represent a function?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Is the given graph a function?

00:05 The definition of a function is that each X value has one Y value

00:10 Let's check the graph values in the table

00:15 We can see that each value has only one Y value, therefore it's a function

00:22 And this is the solution to the question

Step-by-step written solution

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Understand the problem

Does the graph below represent a function?

Step-by-step solution

It is important to remember that a function is an equation that assigns to each value in domain $x$ only one value in range $y$ .

Since we can see that for every $x$ value found on the graph there is only one corresponding $y$ value, the graph is indeed a function.

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic

Definition: Functions assign exactly one y-value to each x-value
Test Method: Draw vertical lines - they intersect graph at most once
Verification: Check any x-value has only one corresponding y-value ✓

Common Mistakes

Avoid these frequent errors

Confusing vertical line test with horizontal line test
Don't use horizontal lines to test for functions = wrong test! Horizontal lines test for one-to-one functions, not functions themselves. Always use vertical lines - if any vertical line intersects the graph more than once, it's not a function.

Practice Quiz

Test your knowledge with interactive questions

Determine whether the following table represents a constant function:

FAQ

Everything you need to know about this question

What exactly is the vertical line test?

The vertical line test helps determine if a graph represents a function. Draw imaginary vertical lines anywhere on the graph - if any vertical line crosses the graph more than once, it's not a function!

Why does this linear graph pass the vertical line test?

Linear graphs like this one are always functions unless they're vertical lines! Since this line has a slope (goes up from left to right), no vertical line can intersect it twice.

What would make a graph NOT a function?

Common examples include:

Circles - vertical lines through the middle cross twice
Parabolas opening sideways - most vertical lines cross twice
Vertical lines themselves - infinite intersections with one vertical line

Can I tell if it's a function without drawing vertical lines?

Yes! For linear equations, if you can solve for $y$ and get $y = mx + b$ form, it's automatically a function. Only vertical lines (like $x = 3$ ) are not functions.

Does the slope of the line matter for the vertical line test?

No! Whether the line goes up, down, or is horizontal doesn't matter. As long as it's not a vertical line, it will always pass the vertical line test and be a function.

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